The invention relates to a method for the closed-loop feedback control of a controlled system having a predetermined set course and a control device for processes having a predetermined set course.
Methods for the closed-loop feedback control of motor drives are sufficiently known. Such controlled systems are used sufficiently in motor vehicles in particular, as in electrically actuated window lifters, seat controls, sliding doors, and/or speed control of wiper systems, for example. In a particular class of these control processes, the set course or a set trajectory of the controlled system is preset. The set course is to be followed repeatedly using the control process or the control device. The individual control processes can hereby be separated by longer time intervals. Such control processes having a predetermined set course are used widely in motor vehicles in particular. In electrically actuated window lifters, seat controls or sliding doors, and in the speed control of a wiper system, for instance.
A multitude of closed-loop feedback controls are made known in the related art. For example P, PI, PID controllers (proportional, proportional+integral, proportional+integral+differential), status controllers, adapter controllers are used for correction purposes along preset set courses. A change in the controlled system (actuator) presents particular difficulties for a control process. The quality of the control process is greatly diminished to a certain extent by changes, such as wear or ageing or parameter fluctuations caused by any other means. More complex control methods (adaption), which can take such changes into consideration, are very limited due to the high requirement on available computer power. Adapter methods often require an overproportionally high cost and material expenditure when used with simple and the simplest control processes in particular.
In light of this related art, the invention is based on the problem of providing a method and a control device that allow simple and reliable closed-loop feedback control of recurrent processes and can thereby take changes and varying influences of the controlled system into consideration.
The problem is solved according to-the invention by a method for the closed-loop feedback control of a controlled system having a predetermined set course and a control trajectory, whereby an output trajectory of the controlled system is measured for the entire closed-loop feedback control time in which the control trajectory is applied to the controlled system, an error of the controlled system is determined as a function of the set course and the output trajectory, and, finally, a new control trajectory is calculated for each instant of a later control process as a function of the error and the control trajectory. This method is based on the approach that a predetermined set course and a first predetermined control trajectory are present.
By comparing the actual output trajectory of the controlled system with the set course, the method according to the invention determines a new control trajectory that draws the output trajectory near to the set course. In this method, the set course and the control trajectory can have values that change over time, as well as constant values. Moreover, transient processes of the controlled system can also be taken into account in the control trajectory.
According to the invention, the output trajectory of the controlled system is measured for the entire closed-loop feedback control time in which the control trajectory is applied to the controlled system. The output trajectory and the set course serve to determine the error. The error is generally a measure of the deviation between the actual and set course of the controlled system. Time shifts/delays and other time-related phenomena of the controlled system can be taken into consideration in the determination of the error. According to the present invention, the new control trajectory is determined individually for every instant of a later control process. A new value of the control trajectory is calculated for a certain instant as a function of the error and the control trajectory, whereby the calculation is based on that error that was determined during application of the control trajectory with the aid of the measured actual values. An advantage of this method is that the great complexity of an adaptive method is avoided. The new control trajectory can be calculated at every instant in a simple manner, whereby no complex analyses, such as wavelet or Fourier transformations, are necessary.
In an embodiment of the method that further reduces the computing effort, the later control process, for which the new control trajectory is calculated, follows the control process in which the error was determined. In other words, the new control trajectory is always calculated for the subsequent control process. As a result, costly assignments between different control processes are avoided. With regard for this process step, it is given that the same set point course is preset again for the subsequent control process.
The computing effort is reduced particularly markedly in an advantageous further development of the method in which the value of the new control trajectory is determined in an instant of the subsequent control process from the values of the closed-loop control error and the control trajectory at an instant of the preceding control process, whereby the same length of time since a beginning instant in which the control trajectory was applied to the controlled system has transpired in the instants of each of the two control processes. Accordingly, the new control trajectory at an instant t is determined from the original control trajectory and the error in an instant t1 from the preceding control interval. This relationship can be illustrated using the following formula:
xe2x80x83uk+m(t)=xcfx86u(uk(t1))⊕xcfx86e(ek(txe2x80x2)),
whereby txe2x88x92Tk+m=txe2x80x2xe2x88x92Tkxe2x80x83xe2x80x83Formula 1:
In this case, Tk and Tk+m represent the start of the kth or the (k+m)th control process, uk (xc2x7) represents the control trajectory of the kth process, ek (xc2x7) represents the error in the kth control process, and uk+m (xc2x7) represents the control trajectory for the (k+m)th control process.
In the advantageous further development of the method, xcfx86u,e are symbols that assign a new value to a value of the control trajectory and/or the error. It proves extremely advantageous for the arithmetical implementation of this process that xcfx86 can be a function. In contrast, xcfx86 is often used as a functional, i.e., as a symbol of a function on a new function, in adaptive methods and/or other closed-loop feedback controls having a preset set course. Such a functional control relationship places high requirements on the control process and its implementation. As mentioned previously, the control relationship above can be simplified further using m=1.
The evaluation of the function values xcfx86u,e can take place using a suitable circuit or a microprocessor. The combination of the function values ⊕ can thereby take place using a suitable selected circuit as well.
In a further simplification of the method, which also reduces the computing effort again and increases the robustness of the calculation, the value of the new control trajectories (uk+1) are determined from the sum of a first and a second value, whereby the first value is only a function of the value of the control trajectory (xcfx86u), and the second value is only a function of the value of the error (xcfx86e) The use of additionxe2x80x94element-wise addition in the case of multicomponent control trajectoriesxe2x80x94leads to a simple implementation of the control relationship with an adder. Moreover, addition has the advantage that detection errors in the determination of the error do not strengthen e, and the method can therefore be designed to be robust.
In the method according to the invention, it proves advantageous to calculate the value of the new control trajectory from the sum of the value of the old control trajectory and the error multiplied by a real factor K. In other words, the function xcfx86u is therefore selected as an identity symbol, and the function xcfx86e is selected as multiplication by a factor K. If multicomponent control trajectories and/or multicomponent errors are considered, element-wise multiplication and element-wise addition take place. In the case of a multicomponent error, a multicomponent real factor K can also be provided, which is multiplied element-wise by the error e.
It has proven appropriate to select the value of the factor Kxe2x89xa70. With a multicomponent factor K, each component is selected greater than zero (xe2x89xa70). In a summary of the further developments of the method according to the invention described above, the following control relationship results:
uk+1(t)=uk(t)+K ek(txe2x80x2),
whereby txe2x88x92Tk+1=txe2x80x2xe2x88x92Tk and Kxe2x89xa70xe2x80x83xe2x80x83Formula 2:
Implementation of such a control relationship is extremely simple, especially since the amplification factor K can be carried out using a simple amplification circuit, and the addition can be carried out using a traditionally known adder.
In a further development of the method, the new control trajectory is calculated after completion of the control process in which the error was determined. This makes it possible to calculate the new control trajectory without a real-time requirement. Since sufficient computing time can be made available between two control processes for the computing process, the method described is an iteratively learning closed-loop feedback control in which no adaptation takes place during the control process.
In an appropriate further development, a predetermined set course can be selected from various predetermined set courses. It must then be taken into consideration that the selected set course must be included in the determination of the new control trajectory. To ensure clarity, the dependence on the set course selectedxe2x80x94which is represented by the error exe2x80x94is not reflected in the formulas above.
It proves to be particularly advantageous to store the set course, control trajectory, and error as sampled time series and to make them available to the method. The sampling rate in this case depends on the process to be controlled and the controlled system. In the method according to the invention, time characteristics can also be processed as functions, of course, either as an explicit time function or an implicit time function that is given as a solution to a differential equation, for example.
It proves appropriate to sample the time series at equal intervals.